{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XB4EQOS3J2JDJKL2AIL3HBOWOS","short_pith_number":"pith:XB4EQOS3","canonical_record":{"source":{"id":"2505.11938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-17T09:57:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"edf42e45011c668b36e2777402cfbeaab9c593a83ee509689736331f4aa27fd4","abstract_canon_sha256":"33742974f5cc690e0d774453a6a94ba7733d69757390e8f1d2c98b145be4e717"},"schema_version":"1.0"},"canonical_sha256":"b878483a5b4e9234a97a0217b385d67489b5cf9518cd7b8cd3ef872353e2e27e","source":{"kind":"arxiv","id":"2505.11938","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.11938","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2505.11938v1","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11938","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"XB4EQOS3J2JD","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"XB4EQOS3J2JDJKL2","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"XB4EQOS3","created_at":"2026-07-05T11:04:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XB4EQOS3J2JDJKL2AIL3HBOWOS","target":"record","payload":{"canonical_record":{"source":{"id":"2505.11938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-17T09:57:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"edf42e45011c668b36e2777402cfbeaab9c593a83ee509689736331f4aa27fd4","abstract_canon_sha256":"33742974f5cc690e0d774453a6a94ba7733d69757390e8f1d2c98b145be4e717"},"schema_version":"1.0"},"canonical_sha256":"b878483a5b4e9234a97a0217b385d67489b5cf9518cd7b8cd3ef872353e2e27e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:55.074223Z","signature_b64":"rOdkPD+zBLpvRwUnX2CUwi0uXZ6Gpjy34emQ/csyxGbPIEuks7EtzXjUk06l50u77kMIEGa/aTJbBLO2phHACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b878483a5b4e9234a97a0217b385d67489b5cf9518cd7b8cd3ef872353e2e27e","last_reissued_at":"2026-07-05T11:04:55.073842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:55.073842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.11938","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6q7dT7rF+qbg9QlnorQ231oecJt7rnUycFnkOzJ4NYealHfGfYvWybFV0C3BFeWVGmZQMIRIXUW78ldAouOUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:49:54.014035Z"},"content_sha256":"d8e002f1f6ec38d8a99edcfc21f5016ca0c9f5ea813993c2249fb2210229f9ea","schema_version":"1.0","event_id":"sha256:d8e002f1f6ec38d8a99edcfc21f5016ca0c9f5ea813993c2249fb2210229f9ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XB4EQOS3J2JDJKL2AIL3HBOWOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable Nonlinear Dynamical Approximation with Dynamical Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Benjamin Caris, Daan Bon, Olga Mula","submitted_at":"2025-05-17T09:57:54Z","abstract_excerpt":"We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and analyzing stability and accuracy of nonlinear dynamical approximations. The parameters of these functions are evolved in time by means of projections on finite dimensional subspaces of an ambient Hilbert space related to the PDE evolution. For practical computations of these projections, one usually needs to sample. We propose a dynamical sampling strategy which c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11938","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.11938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8V9szWzPtGQVTuUoaNCOCEsAxm9gfTkLVl4s6ftS+6FWt6oI7QszR+DKeLwUdv88njkaj5ZTn96mkU+EzthLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:49:54.014434Z"},"content_sha256":"5155a20931dbd5586ee64749db5d137f0c3c0d65e40405267636109a17fb589c","schema_version":"1.0","event_id":"sha256:5155a20931dbd5586ee64749db5d137f0c3c0d65e40405267636109a17fb589c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS/bundle.json","state_url":"https://pith.science/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-06T15:49:54Z","links":{"resolver":"https://pith.science/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS","bundle":"https://pith.science/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS/bundle.json","state":"https://pith.science/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XB4EQOS3J2JDJKL2AIL3HBOWOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XB4EQOS3J2JDJKL2AIL3HBOWOS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"33742974f5cc690e0d774453a6a94ba7733d69757390e8f1d2c98b145be4e717","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-17T09:57:54Z","title_canon_sha256":"edf42e45011c668b36e2777402cfbeaab9c593a83ee509689736331f4aa27fd4"},"schema_version":"1.0","source":{"id":"2505.11938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.11938","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2505.11938v1","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11938","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"XB4EQOS3J2JD","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"XB4EQOS3J2JDJKL2","created_at":"2026-07-05T11:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"XB4EQOS3","created_at":"2026-07-05T11:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:5155a20931dbd5586ee64749db5d137f0c3c0d65e40405267636109a17fb589c","target":"graph","created_at":"2026-07-05T11:04:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.11938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and analyzing stability and accuracy of nonlinear dynamical approximations. The parameters of these functions are evolved in time by means of projections on finite dimensional subspaces of an ambient Hilbert space related to the PDE evolution. For practical computations of these projections, one usually needs to sample. We propose a dynamical sampling strategy which c","authors_text":"Benjamin Caris, Daan Bon, Olga Mula","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-17T09:57:54Z","title":"Stable Nonlinear Dynamical Approximation with Dynamical Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11938","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d8e002f1f6ec38d8a99edcfc21f5016ca0c9f5ea813993c2249fb2210229f9ea","target":"record","created_at":"2026-07-05T11:04:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"33742974f5cc690e0d774453a6a94ba7733d69757390e8f1d2c98b145be4e717","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-17T09:57:54Z","title_canon_sha256":"edf42e45011c668b36e2777402cfbeaab9c593a83ee509689736331f4aa27fd4"},"schema_version":"1.0","source":{"id":"2505.11938","kind":"arxiv","version":1}},"canonical_sha256":"b878483a5b4e9234a97a0217b385d67489b5cf9518cd7b8cd3ef872353e2e27e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b878483a5b4e9234a97a0217b385d67489b5cf9518cd7b8cd3ef872353e2e27e","first_computed_at":"2026-07-05T11:04:55.073842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:04:55.073842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOdkPD+zBLpvRwUnX2CUwi0uXZ6Gpjy34emQ/csyxGbPIEuks7EtzXjUk06l50u77kMIEGa/aTJbBLO2phHACw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:04:55.074223Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.11938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8e002f1f6ec38d8a99edcfc21f5016ca0c9f5ea813993c2249fb2210229f9ea","sha256:5155a20931dbd5586ee64749db5d137f0c3c0d65e40405267636109a17fb589c"],"state_sha256":"998350a40b1e5e92e255c6507617eed694985bd4e037d05d8763f6e35e138d5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rCus4YTF0/3YoKziGygpwBwLbVkUqJQz/F2UrSI0urzfjubGRx6P3MAYc5pk7gR+nBmIKv4SLhNBNH6PDHPsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:49:54.016441Z","bundle_sha256":"6d52ecfc3eb0c710e7da522154ad9bf6d522c48dfe7f2b4b949aa5dbce778f55"}}